The quality of a contractor is very important to the overall outcome of a home kitchen renovation. Online reviews are typically very unreliable, as contractors take steps to control their online image by posting fake reviews of their work. As a result, prior to hiring a contractor, it is impossible for the typical homeowner to determine whether a potential contractor is a "good" contractor or a "bad" one. For a kitchen renovation done by a good contractor, homeowners are willing to pay $80,000. For a renovation done by a bad contractor, they would only be willing to pay $50,000. Good contractors know they are good and have many other alternative projects to work on. As a result, the minimum they are willing to accept to do a kitchen renovation is $60,000. Bad contractors have fewer opportunities and therefore will accept $45,000 to do a renovation.

[2].[a] (5 marks) What price would homeowners be willing to pay for a renovation done by a contractor of unknown quality if the fraction of good contractors in the market was 30 percent. Would this market support renovations done by both types of contractors?

[2].[b] (5 marks) What fraction of good contractors, f, is necessary so that the market for renovations includes those done by good contractors?